Exercise · ZW-CONTINUOUS-FUNCTION-003 · ★★☆ Intermediate
Which value of k makes \(f(x)=\begin{cases}\dfrac{x^{2}-4}{x-2}&\text{if }x\neq2\[2mm] k&\text{if }x=2\end{cases}\) continuous at \(x = 2\)?
Choose one option.
Show answer
- C. \(4\)
Explanation
For f to be continuous at 2, k must equal the limit: \(\lim_{x\to2}\dfrac{x^{2}-4}{x-2}=\lim_{x\to2}(x+2)=4\). So k = 4.
Review the concept: Continuous function
A function \(f\) is continuous at \(a\) if \(f(a)\) is defined, its limit as \(x\) tends to \(a\) exists and equals \(f(a)\).
\[\lim_{x\to a}f(x)=f(a)\]
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